4th International Conference on Business Analytics and Intelligence ... Analysis of the mutual funds ... value) and the capitalization (large, medium or small).
Decomposition of Time Series Data to Check Consistency between Fund Style and Actual Fund Composition of Mutual Funds Jaydip Sen Calcutta Business School, Kolkata, INDIA
4th International Conference on Business Analytics and Intelligence (ICBAI) December 19 - 21, 2016, Bangalore, INDIA
Objective of the Work • The primary objective of the work is to develop a framework for checking the consistency among the actual fund composition and the fund style of several well-known mutual funds in the Indian financial market. • While checking the consistency between the fund styles and the actual fund composition, we have also studied the behavior of the stock prices of various companies constituting the mutual funds.
Outline • • • • • • •
Related work Methodology used Illustrative time series decomposition ` Observations in time series decomposition Computation of statistics from decomposition results Analysis of the mutual funds Conclusion
Related Work • Chevalier & Ellison have argued that while the investors would always prefer the mutual fund companies to use their judgement to maximize the risk-adjusted returns, the fund companies would like to take actions which lead to increase in inflow of investments. • Cremers et al introduce a new measure for portfolio management that represent the share of portfolio holdings that differ from the benchmark index holding. They have also demonstrated how the new measure can be used to predict the performance of a mutual fund. • Zheng studied fund selection ability of aggregate mutual fund investors’ portfolio and observed that investors in aggregate are able to make buying and selling decisions based on good assessment of short-term future performance.
Methodology Used • We choose eight well-known mutual funds in the Indian financial market. • For each mutual fund, we note its portfolio composition and fund style. • For portfolio composition, we have identified the top ten sectors in which the mutual fund allocation has been done and for fund style we have identified the investment style (growth, blend or value) and the capitalization (large, medium or small). • Based on the top holdings of each mutual fund, we have taken a sample of 10 – 15 stocks from the top ten sectors in which fund allocation has been made. • For each stock, we use its daily closing index value in the NSE for the period January 2008 to December 2015. • We compute the monthly average of the index values of each stock and store the monthly average values in a plain text (.txt) file. • Accordingly, for each stock, we create a plain text file containing 96 records (12 records for each year and there are 8 years).
Methodology Used • R library functions are used to convert these raw data points into monthly time series data. • The time series is decomposed into three components – Trend, Seasonal and Random. • We plot the time series and all its three components for each stock so as to get a visual idea about the relative strengths of the components in each time series. • After decomposition, we study the summary characteristics of the stocks in the mutual funds. For each stock, we compute the relative percentages of the trend, seasonal and random components with respect to its aggregate price. • The summary of the decomposition results is then compared with the fund style and the capitalization of the fund to verify whether the fund style is consistent with the fund composition.
An Illustrative Time Series
HDFC Bank Stock Price Time Series (Jan 2008 – Dec 2015)
Time Series Components
HDFC Bank Stock Price Time Series Components (Jan 2008 – Dec 2015)
Observations • Trend values are not available for the period Jan 2008 – June 2008 and Jul 2015 – Dec 2015 since the trends are computed based on 12 month moving averages. • The random component values are also missing for the same period. • The HDFC Bank time series is strongly dominated by the trend component with the presence of mild seasonal and random components. • The weakest seasonality is observed in the month of February and the highest seasonality is observed in the months of July and October. • The mean percentages of trend, seasonality and random components are 101, 0.01 and 1.20 respectively.
Computations • After the time series decompositions are carried our for all stocks, the significance of the decomposition results are done using F test. • All decomposition results are found to pass the F test. • For the purpose of understanding the relative strengths of the three components, in time series we compute four statistics: (i) Max, (ii) Min, (iii) Mean, (iv) SD of the percentage values of each component. • Since random and seasonal percentages can be negative for certain months, for computing mean, we ignore the signs. In other words, we compute the mean of their absolute values so that mean reflects the mean of their magnitudes. • We consider a component as a “dominant” component in a time series if its mean percentage exceeds the threshold value of 15. (Rob J Hyndman)
Mutual Funds We studied the following mutual funds: 1. UTI Infrastructure Fund Fund Style: Growth, Capitalization: Medium.
2. ICICI Prudential Infrastructure Fund Fund Style: Blend, Capitalization: Medium
3. Axis Midcap Fund Fund Style: Growth, Capitalization: Medium
4. ICICI Prudential Value Discovery Fund Fund Style: Blend, Capitalization: Large
5. ICICI Prudential Focused Bluechip Equity Fund Fund Style: Growth, Capitalization: Large
6. UTI Long-Term Equity Fund Fund Style: Growth, Capitalization: Large
7. Reliance Small Cap Fund Fund: Growth, Capitalization: Small
8. UTI Bluechip Flexicap Fund Fund: Growth, Capitalization: Large
Results UTI Infrastructure Fund
Infrastructure Fund with stocks having medium capitalization is expected to have presence of trend, seasonal and random components. The results validate this.
Results ICICI Prudential Infrastructure Fund
Infrastructure Fund with stocks having medium capitalization is expected to have presence of trend, seasonal and random components. The results validate this.
Results Axis Midcap Fund
Growth funds are expected to have stocks more dominated by trend components. However, since the fund focuses on “medium” capitalization, some of the stocks have the presence of random components.
Results ICICI Prudential Value Discovery Fund
Value discovery funds with “blend” fund style and “medium” capitalization is expected to have stocks more dominated by trend components. However, in short term, some stocks may also exhibit random and seasonal behavior, The results validate this.
Results ICICI Prudential Focused Bluechip Equity Fund
A fund with “growth” style and “large” capitalization should only include stock having strong trend component. Hence, here we find four inconsistent stocks having significant random and seasonal components.
Results UTI Long-Term Equity Fund
Growth fund with large capitalization should only include stock having strong trend component. Hence, here we find four inconsistent stocks having significant random components.
Results Reliance Small Cap Fund
A fun with “growth: style and “small” capitalization should mostly consist of stocks with dominant random component/ While we observe all the stocks in sample have strong random components, HDFC bank has only a strong trend component. HDFC Bank stock is inconsistent with the fund style. Possibly it has been included keeping in mind the “growth” style of the fund.
Results UTI Bluechip Flexicap Fund
A fund with “growth” fund style and a “large capitalization” should include stocks having strong trend components. Even though it is a “flexicap” fund, number stocks having random components seems to be quite high.
Conclusion • We have presented a novel approach for checking the consistency between the style of a mutual fund and its actual fund composition. • Our approach is based on decomposition of the time series of individual stocks in a fund. The decomposition results provide several useful insights that are suitably aggregated by several statistical computations and tests to obtain an overall idea about the fund. • While we have applied our technique only to equity funds the same can be applied to debt funds as well.
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